In the case of the AD social norm (that generates the highest levels of cooperation), pure strategies are largely abandoned in favour of conditional strategies. Among the 8 conditional strategies, only two are adopted by a sizeable part of the population: C\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\)  and D\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\) .
These are strategies that share a common goal: to participate in interactions with a population of agents who are sufficiently cooperative (since they both set the reputational threshold for participation in their group to 0). However, while the former strategy wishes to engage with and enjoy the collaboration of their peers, the latter aims to exploit them. When this is not possible, both strategies act as a loner for a lower but guaranteed payoff. From the transition table (SM Fig. S1, left panel), it emerges that most strategies turn into either C\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\)  or D\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\) , and that these two strategies are much more likely to turn into each other than anything else (leftmost panel of Fig. REF ). This is a consequence of the interaction of these strategies and the level of cooperation in the population. This effect can be clearly discerned studying the temporal evolution of the proportion of agents playing these two strategies and of the associated actions played (Fig. S14, panel C). While the proportion of D\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\)  and C\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\)  in the population move systematically in opposite directions, studying the actual actions played we observe oscillations in the proportion of opt-out and cooperative actions, while defection is played by fewer individuals in a stable manner. In other terms the C\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\)  strategy uses the reputational information to conditionally cooperate. When in a group there happens to be too many defectors (most of whom are D\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\) s given their relative prevalence) the strategy resorts to opting out, and thus avoiding being exploited. The strategy D\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\)  acts similarly, thus avoiding being completely evolved out, but it is unable to spread the defection in the population. Importantly, this dynamic relies on the fact that under the AD social norm, agents playing defection are assigned a strictly worse reputation than loners, thus allowing C\(^{\mbox{\tiny 0,L}}_{\mbox{\tiny }}\)  to discriminate between the two behaviours. In other terms, the cyclic behaviour of the baseline model - described by [1]} - reemerges, but with the loner strategy being part of two more complex conditional strategies. Importantly, the cycles are - in this setup - quite noisy due to the occasional attractiveness (Fig. SREF , left panel) of other strategies, which allows them to be the destination of some transitions and thus to survive albeit in low numbers.
